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Unformatted text preview: Section 3.7 One-to-One Functions and Their Inverses Page 1 of 18 Example 1: Determine whether the function f ( x ) = 2 x + 3 is one-to-one. If the function is one-to-one, find its inverse function. Solution to Example 1: Section 3.7 One-to-One Functions and Their Inverses Page 2 of 18 Section 3.7 One-to-One Functions and Their Inverses Page 3 of 18 Example 2: Determine whether the function f ( x ) one-to-one, find its inverse function. x 2 2 is one-to-one. If the function is Section 3.7 One-to-One Functions and Their Inverses Page 4 of 18 Example 3: Use the Property of Inverse Functions to show that 5 ( )2.60 0 2 -1.16 45 (()-512 7CInve5htno2>Tw1(un(((w1(un33 scn0 5 and Section 3.7 One-to-One Functions and Their Inverses Page 5 of 18 Example 4: The graph of a one-to-one function y of f 1. f ( x) is shown below. Sketch the graph Section 3.7 One-to-One Functions and Their Inverses Example 5: Page 6 of 18 Section 3.7 One-to-One Functions and Their Inverses Solution to Example 5: Page 7 of 18 Section 3.7 One-to-One Functions and Their Inverses Example 6: Solution to Example 6: Page 8 of 18 Section 3.7 One-to-One Functions and Their Inverses Page 9 of 18 Section 3.7 One-to-One Functions and Their Inverses Page 10 of 18 Section 3.7 One-to-One Functions and Their Inverses Example 7: Solution to Example 7: Page 11 of 18 Section 3.7 One-to-One Functions and Their Inverses Page 12 of 18 Section 3.7 One-to-One Functions and Their Inverses Example 8: Solution to Example 8: Example 9: Page 13 of 18 Section 3.7 One-to-One Functions and Their Inverses Solution to Example 9: Example 10: Solution to Example 10: Page 14 of 18 Section 3.7 One-to-One Functions and Their Inverses Page 15 of 18 q 6 4 0 5 2 3 ) x(xf 6)( 4)( Exercise Set 3.7: Inverse Functions Ee03Sav•`…6PDpFQd„cf„cpFf„dpFx„dpF•Ub`uV2hpUVR`bi„ A€V’„…–$S`HU0rfy!9&i0@f“!D'eB•bvQdtaPC`p„6Wc€A‡H&i0faQ&av•fcQD&f0€rfaQh&c0@rf3fVe0`pfSAf(Ui„f(U`bdpV!fWUe QfWUcb`puVhpUVI„f‡Ud•GTi„pFx„qTf`G€FH„q0TcQd6PD#avr•bef& 0a•DefFR&a•2e †a•2e †`•Df"fFRf`•&R†fb †g•D`‚fyFQfVQ†`…f`Ipf`I`pca…•$bˆe”g`Idecˆ"ga$–p€6Iˆ†h€e ‚d•8 † 8 €`8 €†Q‚f‚†f‚B†H9ffHbfgd@‚&`Prdpei4"f•ra(`fI(`f€’†Fˆap4ec`f8ˆc`fˆdpP–†GFehe`dPT†VF%Hgp`T†wFD(d@‚fGB!De@‚"pF$f‚"`†d0‚!(€fd0‚!(€f40‚!F&Cb"dP–pX x‚pXed"`b† "†D(6GB0d1A€cp˜#P–@r`&‚vhA#PvfP–ƒvbA#fB1•vc€‚$`dhBF6"B7‚p˜$c`eD†UfEhFUf„@hFUf„hFUfehFw†6HF&…fHF…f5"Qf5%pdPrQf"PrQdg‚Q(€dfp˜%ˆFV‚QEdc€P3–…S6TrB`2e”†&5@a"1g‚a0g€‚a0g‚a07‚E1d&Ps„B`veha`vBPrabT†)c‚&fHv)bˆT‡`†7‚&g‚v6(e`˜'c†HD‡iTd@rUP$ta T‡g@f5'hPfWrv…&bˆTpaV‚•%f€˜(PVD‚•%`ˆF–HE„h@TˆPFH•X€$d%(E#˜†1r&7‚h‚‘`˜)€!&0H„Eg T‰Pr0!a T‰&‡H‘`d„b€@t–7†˜VIa6 ˜`c†rFDfFDcFUfFUg`Ftge€T`g@v(F†gb€T`h`f7†Fh`˜apfV†fd@˜a`f†(€` ˜aˆVrFEX€T‡xFpTa€d`ˆF(e06h`˜fe`˜b€6D†!a@ ˜bg TbPt!BF`0€g a Tbg av†&„Ae€Tbh@t(F6`Tc†g@˜catD†6b` ˜cd@p–rF6VfF6Vd Tcg@p–0Tcg@p•Tch`†‡F6epTc7d(A04b€vf"4d`vD ƒFc"4e€`v ƒFXe“p`fr“Fp`fr“Fˆf“FˆcP`fFP`Tea `V‡FepTcdA `V4FBAefh`˜efgAefgAeg `Fb ƒVrdAeh@pF2 ƒV„b ƒf`"6 p6Qa@r“ff“f2d€H6c p60Hd@ƒfD`a6ep“fVhpTfg@p&v†ftepTfh`p&Ff†cAfcp!Ff7Ag`!Fqd•’7b€`t†v(f•’7d`D#vFc•e€9Xipˆ“ x8d x8fF†0`H8ca€d `ƒ†BThg!Y–v†r™g`i Y–F†™d`ia@4‘&VeI#t˜•’9h`Y†t–7˜g@&˜f•’Fb€Y†i$f(˜e$fpY†P’Fh€Y†9$r˜c•’Ah@Y†P’Bab`i$&D˜f•’Be`Y†t„&˜g@Bg@Y†™$&˜i•’Bcp–„6a`Cb€(edXf@Cg™g`Ch€Y–‡D6ˆ`TaHcdfDFBg€TDd `•TDfiDF`$rc•’h@pD$F„f•’E` pt„Vi•’Ea@!D`&4QdWg`E`p&‡DQVa€H@60„†f”Q†g a`3!&v@fa x xxg 1 (A x f −1 Exercise Set 3.7: Inverse Functions Exercise Set 3.7: Inverse Functions 45. f (x ) = 2x + 3 x−4 46. f ( x) = 3 − 8x x+5 47. f ( x) = 7 − 2 x 48. f ( x) = 2 + 6 x + 5 Use the Property of Inverse Functions to determine whether each of the following pairs of functions are inverses of each other. Explain your answer. 49. f ( x) = 4 x − 1 ; g ( x) = 1 4 50. f ( x) = 2 + 3x ; g ( x) = x−2 3 51. f ( x) = 52. 4− x ; 5 f ( x) = 2 x + 5 ; x +1 g ( x) = 4 − 5 x g ( x) = 1 2x + 5 53. f ( x) = x3 − 2 ; g ( x) = 3 x + 2 54. f ( x) = 5 x − 7 ; g ( x ) = ( x + 7 )5 55. f ( x) = 5 ; x g ( x) = 5 x 56. f ( x) = x 2 + 9, x ≥ 0 ; g ( x) = x − 9 , x ≥ 9 Answer the following. 57. If f ( x) is a function that represents the amount of revenue (in dollars) by selling x tickets, then what does f −1 (500) represent? 58. If f ( x) is a function that represents the area of a circle with radius x, then what does f −1(80) represent? ...
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